# Power statistics-equivalent finite groups

From Groupprops

This article defines an equivalence relation over the collection of groups. View a complete list of equivalence relations on groups.

## Definition

Two finite groups are termed **power statistics-equivalent finite groups** if their power statistics functions are identical.

## Facts

### Relation with group properties

Note that the third column (first question column) is the conjunction of the fourth and fifth columns.

Group property | Finite version | Is any group power statistics-equivalent to a group with this property isomorphic to it? | Does any group power statistics-equivalent to a group with this property also have this property? | Are any two groups with this property that are power statistics-equivalent also isomorphic? |
---|---|---|---|---|

Cyclic group | Finite cyclic group | Yes | Yes | Yes |

Abelian group | Finite abelian group | No | No | Yes: Finite abelian groups with the same power statistics are isomorphic |

Nilpotent group | Finite nilpotent group | No | ? | No |

## =Relation with other relations

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